👉Tension zone and compression zone of a beam

🚧When a beam bends under load its cross-sectional fibers (top to bottom) stretch or shorten.

🏷That creates two zones:

⭐️Tension zone

⏺The part of the section where fibers are being stretched (pulled).
⏺Stretched fibers develop tensile stress.

⏺In reinforced concrete beams the steel reinforcement is placed in the tension zone because concrete is weak in tension but steel is strong in tension.
⏺Tension causes cracks (in concrete) when tensile stress exceeds tensile capacity.

⭐️Compression zone

⏺The part of the section where fibers are being shortened (squeezed).
⏺Fibers develop compressive stress.

⏺Concrete handles compression well, so the compression zone is mainly resisted by the concrete (and sometimes by compression reinforcement).
⏺Failure in compression shows as crushing of concrete if overload occurs.

⭐️Neutral axis

⏺The horizontal line inside the cross section that separates the two zones.

⏺Fibers on the neutral axis neither stretch nor shorten (zero strain/stress).
⏺Distance from neutral axis to extreme fiber is used in stress calculations.

❇️How it appears in common cases

⏺A simply supported beam loaded downward (sagging): top fibers → compression, bottom fibers → tension.
⏺A cantilever or overhanging span under certain loads (hogging): top may be in tension and bottom in compression — depends on bending moment sign.

🚧Basic formula (bending stress sign)

⏺Bending stress formula:
sigma = (M * y) / I
Where
sigma = bending stress
M = bending moment
y = distance from neutral axis
I = moment of inertia
Tension and compression rule:
If sigma is positive →

⚡️TENSION

⏺If sigma is negative → COMPRESSION
▶️(Note: sign depends on bending direction)

❇️Neutral axis condition:
stress at neutral axis = 0
y = 0
❇️Maximum bending stress:
sigma_max = (M * y_max) / I

🔰For rectangular beam section: Moment of inertia:
I = (b * h^3) / 12

Where
b = width of beam
h = total depth of beam
Stress at extreme fibers:
Top fiber stress: sigma_top = (M * h/2) / I

🎲Bottom fiber stress: sigma_bottom = (M * h/2) / I
(Sign decides tension or compression)

🚧Reinforced concrete design concept (basic):

▶️Compression force in concrete: C = 0.36 * fck * b * x
▶️Tension force in steel: T = 0.87 * fy * Ast
▶️Equilibrium condition: C = T


⏺Positive means tension (convention depends on sign choices), negative means compression — importantly the sign changes across the neutral axis.

📜Design insight (reinforced concrete)

⏺Put main steel where tension occurs (to carry tensile forces and control cracking).

▶️Depth of compression zone controls the beam’s capacity; designers check that compression concrete and tension steel balance properly.

@etconp